1. Technical Field of the Invention
The invention relates generally to communication systems; and, more particularly, it relates to decoding of signals employed in such communication systems.
2. Description of Related Art
Data communication systems have been under continual development for many years. One such type of communication system that has been of significant interest lately is a communication system that employs iterative error correction codes. Of particular interest is a communication system that employs LDPC (Low Density Parity Check) code. Communications systems with iterative codes are often able to achieve lower bit error rates (BER) than alternative codes for a given signal to noise ratio (SNR).
A continual and primary directive in this area of development has been to try continually to lower the SNR required to achieve a given BER within a communication system. The ideal goal has been to try to reach Shannon's limit in a communication channel. Shannon's limit may be viewed as being the maximum achievable data rate to be used in a communication channel, having a particular SNR (Signal to Noise Ratio), that achieves error free transmission through the communication channel. In other words, the Shannon limit is the theoretical bound for channel capacity for a given modulation and code rate.
LDPC code has been shown to provide for excellent decoding performance that can approach the Shannon limit in some cases. For example, some LDPC decoders have been shown to come within 0.3 dB (decibels) from the theoretical Shannon limit. While this example was achieved using an irregular LDPC code of a length of one million, it nevertheless demonstrates the very promising application of LDPC codes within communication systems.
The use of LDPC coded signals continues to be explored within many newer application areas. For example, the use of LDPC coded signals has been of significant concern within the IEEE (Institute of Electrical & Electronics Engineers) P802.3an (10GBASE-T) Task Force. This IEEE P802.3an (10GBASE-T) Task Force has been created by the IEEE to develop and standardize a copper 10 Giga-bit Ethernet standard that operates over twisted pair cabling according the IEEE 802.3 CSMA/CD Ethernet protocols. Carrier Sense Multiple Access/Collision Detect (CSMA/CD) is the protocol for carrier transmission access in Ethernet networks. IEEE 802.3an (10GBASE-T) is an emerging standard for 10 Gbps (Giga-bits per second) Ethernet operation over 4 wire twisted pair cables. More public information is available concerning the IEEE P802.3an (10GBASE-T) Task Force at the following Internet address:                “http://www.ieee802.org/3/an/”.        
This high data rate provided in such applications is relatively close to the theoretical maximum rate possible over the worst case 100 meter cable. Near-capacity achieving error correction codes are required to enable 10 Gbps operation. The latency required by using traditional concatenated codes, simply preclude their use in such applications.
Clearly, there is a need in the art for some alternative coding type and modulation implementations that can provide near-capacity achieving error correction.
One such type of codes, of the possible codes that achieve very good performance that approaches the theoretical limits, is that that may be characterized as being LDPC codes. Such a code offers the combination of low latency and high coding gain necessary to enable 10GBASET Ethernet transceiver PHY (physical layer) products.
When considering a coding system that codes the binary information sequence to an LDPC codeword and then maps the LDPC codeword to constellation signals. These constellation signals may also be viewed as being modulation signals as well. A modulation may be viewed as being a particular constellation shape having a unique mapping of the constellation points included therein.
In a multi-path communication system (e.g., where the communication channel itself is composed of multiple wires, multiple channels, and/or multiple paths), it may be supposed that the channel noise of each wire, channel, and/or path can be modeled as being AWGN (Additive White Gaussian Noise) with noise variance, σ2. This assumption is not restrictive since an optimal receiver will “whiten” non-AWGN in the channel such that the noise will closely approximate AWGN when seen by the LDPC decoder.
Then, upon receiving the symbol, y, the probability that the constellation signal, s, in the constellation was actually sent is provided as follows:
                                          p            s                    ⁡                      (                          y              ❘              s                        )                          =                              1                          σ              ⁢                                                2                  ⁢                  π                                                              ⁢                      exp            ⁡                          (                                                                    -                    1                                                        2                    ⁢                                          σ                      2                                                                      ⁢                                                      D                    SE                                    ⁡                                      (                                          y                      ,                      s                                        )                                                              )                                                          (                  EQ          ⁢                                          ⁢          1                )            where DSE(y,s) is the squared Euclidean distance between the transmitted signal, y, and the received signal, s, and σ2 is the variance of the AWGN. The value of this probability, ps(y|s), may be referred to as the metric of the received signal, s. Based on this probability (or alternatively referred to as this metric), the MLD (Maximal Likelihood Decoding) approach tries all of the possible codewords with (EQ 1) for all possible symbols, s, and then the MLD approach finds the one codeword that has the maximal total probabilities. However, due to the inherent complexity of MLD approach, it is not possible with today's technology to carry out MLD when decoding LDPC coded signals or other such ECCs (Error Correcting Codes).
One of the sub-optimal decoding approaches (with respect to decoding LDPC coded signals or other such ECCs) is the iterative MP (Message Passing) (or BP (Belief Propagation)) decoding approach. In this MP (or BP) approach, the above provided (EQ 1) is used as a transition metric.
Moreover, in a practical realization of a communication system whose communication channel includes multiple wires, it is noted that the noise variance, σ2, of each of the wires may differ significantly from one another. This difference in noise among each of the various and distinct components of the communication channel (e.g., wires, channels, and/or paths) presents a difficulty in calculating the value of this probability, ps(y|s), which again may be referred to as the metric of the received signal, s.
Clearly, there is a need in the art to provide for additional and improved means by which the varying degrees of noise within each of the multiple wires may be handled to provide for improved performance. A significant component of such a need lies in the calculation of the calculation of the probability, ps(y|s), which may be viewed as being the symbol metric of the received signal, s.